Spectral Representation of Discrete-Time Stationary Signals and Their Computer Simulations

  • Wojbor A. Woyczyński


Given an arbitrary power spectrum S X (f) or, equivalently, its inverse Fourier transform, the autocovariance function γx(τ), our ability to simulate the corresponding stationary random signals X(t), using only the pseudo-random number generator, which produces, say, discrete-time white noise, depends on the observation that, in some sense, all stationary random signals can be approximated by superpositions of random harmonic oscillations such as those discussed in Examples 4.1.2 and 4.1.9.


Power Spectrum White Noise Spectral Density Power Spectral Density Spectral Representation 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Statistics and Center for Stochastic and Chaotic Processes in Sciences and TechnologyCase Western Reserve UniversityClevelandUSA

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